# How do you simplify the expression (x^5y^-8)/(x^5y^-6) using the properties?

Aug 22, 2017

See a solution process below:

#### Explanation:

First, we can use these two properties of exponents:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$ and ${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$

$\frac{{x}^{\textcolor{red}{5}} {y}^{\textcolor{red}{- 8}}}{{x}^{\textcolor{b l u e}{5}} {y}^{\textcolor{b l u e}{- 6}}} \implies {x}^{\textcolor{red}{5} - \textcolor{b l u e}{5}} / {y}^{\textcolor{b l u e}{- 6} - \textcolor{red}{- 8}} \implies {x}^{\textcolor{red}{5} - \textcolor{b l u e}{5}} / {y}^{\textcolor{b l u e}{- 6} + \textcolor{red}{8}} \implies {x}^{0} / {y}^{2}$

We can use this property to simplify the $x$ term:

${a}^{\textcolor{red}{0}} = 1$

${x}^{\textcolor{red}{0}} / {y}^{2} \implies \frac{1}{y} ^ 2$